1
Q
Sum of squares of errors
A
2
Q
Find LSE
A
NEED TO FIND MIN OF sum of squares of errors
- partial deriv w respect to β0, β1;
-equate to zero (obtain normal eqs)
-calc 2nd deriv
-form hessian
3
Q
For lse of sum of squares errors
A
4
Q
For Lse,
A
5
Q
A
6
Q
A
7
Q
Terms of c_i
A
8
Q
A
9
Q
A
10
Q
A
11
Q
A
12
Q
Normal equations obtained from lsm given by (matrix form)
A
13
Q
Unique solution to normal equations obtained from lsm (vector)
A
14
Q
Lsm β^ is?
A
Unbiased
15
Q
Variance matrix of β^ (vector)
A
16
Q
Prove that β^- is unbiased
A
17
Q
Prove var matrix of β^
A
18
Q
Vector of null model
A
19
Q
β^ in null model
A
20
Q
Var[β^] in null model?
A
21
Q
β^ in no intercept model?
A
22
Q
Var[β^] in no intercept model?
A
23
Q
LSE β^- (vector) given by?
A
24
Q
Limitation of β^- vector estimator?
A
25
Estimation of β by least squares; S=?
Sum of squares, which then needs to be minimised
26
Estimation of β; normal equations?
27
Estimation of β; unique solution to normal equations?
28
Then β^ ~?
29
Gauss Markov Theorem
30
BLUE
Best Linear Unbiased Estimator . Estimator, among all unbiased estimators of form (image) that has smaller variance
31
32
33
c_i
